Question

6.

Digital Inc. is evaluating two different operating structures which are described below. The firm has annual interest expense of $500, common shares outstanding of 4,000, and a tax rate of 35 percent.

Fixed Cost Price per Unit Variable Cost per Unit Operating Structure 1: $1,000 $3 $2.20 Operating Structure 2: $2,500 $3 $2.00 (a) For each operating structure, calculate: EBIT and EPS at 10,000, 20,000, and 30,000 units. the degree of operating leverage (DOL) and degree of total leverage (DTL) using 20,000 units as a base sales level. the operating breakeven point in units. (b) Which operating structure has greater operating leverage and business risk? (c) If China America projects sales of 20,000 units, which operating structure is recommended?

Answer 1

a)

Operating Structure 1

Units	10,000	20,000	30,000
Sales @3 per unit	30,000	60,000	90,000
Less: Variable cost @2.20 per unit	22,000	44,000	66,000
Less: Fixed costs	1,000	1,000	1,000
EBIT	7,000	15,000	23,000
Less: Interest expense	500	500	500
EBT	6,500	14,500	22,500
Less: Tax@35%	2,275	5,075	7,875
Net Income (i)	4,225	9,425	14,625
No. of shares (ii)	4000	4000	4000
EPS ( i / ii )	1.05625	2.35625	3.65625

Degree of Operating leverage (DOL) = % change in EBIT / % change in Sales

Taking 10,000 as base and 20,000 as the incremental level, we have -

% change in Sales = (60,000 - 30,000) / 30,000 = 1 or 100%

% change in EBIT = (15,000 - 7,000) / 7,000 = 1.14285714285 or 114.285714285%

DOL = 114.285714285% / 100% = 1.14285714285 or 1.14

Degree of Total Leverage (DTL) = % change in EPS / % change in sales

Taking 10,000 units as base and 20,000 units as increment, we have -

% change in EPS = ($2.35625 - $1.05625) / $1.05625 = 1.23076923076 or 123.076923076%

DTL = 123.076923076% / 100% = 1.23076923076 or 1.23

Operating break even point = Fixed Costs / (Sales price - Variable cost per unit) = $1000 / ($3 - $2.2) = 1250 units

Operating Structure 2

Units	10,000	20,000	30,000
Sales @3 per unit	30,000	60,000	90,000
Less: Variable cost @2 per unit	20,000	40,000	60,000
Less: Fixed costs	2,500	2,500	2,500
EBIT	7,500	17,500	27,500
Less: Interest expense	500	500	500
EBT	7,000	17,000	27,000
Less: Tax@35%	2,450	5,950	9,450
Net Income (i)	4,550	11,050	17,550
No. of shares (ii)	4000	4000	4000
EPS ( i / ii )	1.1375	2.7625	4.3875

Degree of Operating leverage (DOL) = % change in EBIT / % change in Sales

Taking 10,000 as base and 20,000 as the incremental level, we have -

% change in Sales = (60,000 - 30,000) / 30,000 = 1 or 100%

% change in EBIT = (17,500 - 7,500) / 7,500 = 1.333333333 or 133.3333333%

DOL = 133.3333333% / 100% = 1.333333333 or 1.33

Degree of Total Leverage (DTL) = % change in EPS / % change in sales

Taking 10,000 units as base and 20,000 units as increment, we have -

% change in EPS = ($2.7625 - $1.1325) / $1.1325 = 1.43929359823 or 143.929359823%

DTL = 143.929359823% / 100% = 1.43929359823 or 1.44

Operating break even point = Fixed Costs / (Sales price - Variable cost per unit) = $2500 / ($3 - $2) = 2500 units

b) Operating structure 2 has greater operating leverage and business risk as it higher DOL due to higher fixed costs.

c) Operating structure 2 is recommended at 20000 units, since it increases the earning per share as well as EBIT which means greater value for the shareholders.